A new fourth‐order numerical algorithm for a class of three‐dimensional nonlinear evolution equations

In this article, a new compact alternating direction implicit finite difference scheme is derived for solving a class of 3-D nonlinear evolution equations. By the discrete energy method, it is shown that the new difference scheme has good stability and can attain second-order accuracy in time and fourth-order accuracy in space with respect to the discrete H1 -norm. A Richardson extrapolation algorithm is applied to achieve fourth-order accuracy in temporal dimension. Numerical experiments illustrate the accuracy and efficiency of the extrapolation algorithm. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013

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